Prediction of jet mixing noise in flight from static tests Ulf Michel CFD Software Entwicklungs- und Forschungsgesellschaft mbH Berlin 22nd AIAA/CEAS Aeroacoustics Conference Lyon, France, 30 May – 1 June 2016

AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016 Introduction Influence of flight velocity on jet noise very important Example: Engine noise tests performed on static test beds Take-off certification noise levels must be predicted correctly for Mf = 0.26 … 0.28 Cruise noise must be known (noise in rear cabin dominated by jet noise) for Mf = 0.78 … 0.85 Flight effect on jet mixing noise has surprising properties Noise is much louder in flight than to be expected from reduced relative velocity. Frequency is not reduced in flight as to be expected from smaller relative velocity. Frequency is Doppler-shifted for observers on the ground, indicating a source that is stationary relative to the nozzle. Noise level is almost unchanged in forward arc for take-off flight Mach numbers. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Industry standard for flight effect prediction Industry standard for modeling the effect of flight speed is using a relative velocity exponent m(θe) m(θe) determined with flight simulations of model jets in free-jet tunnels re is wave-normal distance (flyover: observer distance at emission time) Predicted noise levels for cruise Mach numbers much too low Relative velocity exponent approach too simple, does not describe physics properly. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Theoretical analysis of flight effect Acoustic analogy in a uniform flight stream best described with convective wave equation for the pressure (Michalke & Michel 1979) Nozzle fixed coordinate system: Source field stationary random Emitted acoustic field also stationary random Integration boundaries stationary Source term q can be approximated by quadrupole and dipole sources (Morfey 1973) AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Integral solution of convective wave equation Green function for radiation into free space (differs in Doppler factor Df from normal wave equation, re is wave-normal distance) Solution in acoustic far field Qq and Qd are quadrupole and dipole source terms for the acoustic far field (see paper) Both integrals yield forward arc amplification (Df-n) Amplification larger for quadrupole than for dipole noise. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Power-spectral density in acoustic far field Time averaged quantities are of interest Jet noise sources non-compact Source interference effects dominate directivity (Michel 2007, 2009) Source interference can only be studied in frequency domain Power-spectral density in acoustic far field consists of four terms conjugate complex Cross-spectral densities between quadrupole and dipole contributions cannot be neglected since they are both dominated by the same instability wave motions in the jet. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Power-spectral density in geometric far field Power-spectral density of quadrupole noise Power-spectral density of sources All interference effects with neighboring source positions are contained in interference integral Gqq Ψs: Phase of source cross spectral density (wavelike motion) Ψr: Phase due to retarded time difference AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Influence of interference integral Source interference explains Directivity of jet mixing noise (Michel 2007, 2009, Michel & Ahuja 2014) Deviation of Mach number exponent from theoretical values 8 (quadrupole noise) and 6 (dipole noise) at 90° to jet axis (see paper) Directivity of broadband shock noise (Michel 1995) Peak frequency and width of peak of broadband shock noise (Michel 1995) AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Decomposition into azimuthal components Source field and far field can be decomposed into azimuthal components Each component m in the far field depends only on the same component in the source field (for jets with axisymmetric mean flow, Michalke 1972) Power-spectral density in far field composed of azimuthal components AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Stretching of flow field in flight Flow field stretched by influence of flight stream Same normalized flow quantities located further downstream in a flight stream Coherence field also stretched Stretching factor Take-off σ ≈ 1.3 Cruise σ ≈3.0 … 4.0 AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Influence of jet stretching Stretching factor result of instability analysis (Michalke & Hermann 1982) Normalizations (indicated by star) Normalized axial source position Normalized axial source length scale Normalized axial coherence length scale Normalized radial source length scale unaffected by stretching Normalized frequency (result of instability analysis) AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Normalization of source strength Normalized quadrupole source strength Normalized dipole source strength Assumptions: Normalized source quantities independent of jet and flight Mach numbers Normalized turbulence quantities independent of jet and flight Mach numbers Normalized mean velocity profiles independent of jet and flight Mach numbers Decomposition into azimuthal components independent of jet and flight Mach numbers All sources are located on circular cylinder with radius rs= Dj/2 AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016 Azimuthal components Solution for one component m of mean square sound pressure due to quadrupole sources in geometric far field: Interference function Azimuthal Interference Axial Interference integral Interference effects are described by azimuthal interference function Jm and axial interference integral Fqqm AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Mean square sound pressure Quadrupole sources Quadrupole-dipole sources Interference integrals, (azimuthal and axial interference), assumed to be identical for all three sources (wave-like sources) Dipole sources Main difference: power of (Mj-Mf)/Df Michalke & Michel proposed to carry out static experiments for Mach number Me= (Mj-Mf)/Df and multiply results with σ3 Df2 Condition: interference integrals only functions of Me (not completely satisfied) Prediction valid for any combination of quadrupole and dipole sources. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Comparison with Aérotrain data Predictions (Michalke & Michel 1979) in comparison with experimental data Dotted lines indicates range with extrapolated static data. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Comparison with Aérotrain data Predictions (Michalke & Michel 1979) in comparison with experimental data Dotted lines indicates range with extrapolated static data. AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Extrapolations of static Aérotrain data Interpolation of static directivities Available range Mj=1.09 to 1.49 Extrapolation to smaller and larger Mach numbers by use of Mach number exponent Extrapolation to small Mach numbers obviously non-physical Peak in rear arc outcome of Helmholtz number scaling through wave refraction (Michel & Ahuja 2014) AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Prediction of cruise noise Cruise noise louder than static noise (reduced ambient pressure not considered) Cause: jet stretching Predictions with relative velocity exponents m yield noise reduction for 90 degrees. (m=3 yields noise level reduction by 10.8 dB for cruise Mach number 0.84, m=4 yields reduction by 14.4 dB) AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Interference integral Assumption was that interference integral G depends only on Me Definition Azimuthal Interference Azimuthal interference depends on Axial interference depends on AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Axial source interference Axial interference function Rear arc: all sources almost in phase (“super directivity”) Other angles: radiation decreased due to oscillating sign of integrand Oscillations get stronger in the forward arc and for higher jet speeds This behavior has led to the proposal that rear arc radiation is caused by large scales, while all other angles are results of fine scale) + - Integrand as function of normalized separation ξc AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

Scaling for axial source interference Condition for identical axial source interference Mach number of static jet must be larger by stretching factor σ. Higher levels in rear arc Lower levels in forward arc. Ms=σ Me Applied to dipole noise only Ms=Me AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016 Conclusion Jet mixing noise in a flight stream can be predicted well with the method of Michalke and Michel (1979). Method only based on Lighthill theory with no arbitrary constant. Small errors in forward and rear arc are results of incorrect modelling of the axial and azimuthal source interference. Levels in forward arc slightly overpredicted, in rear arc slightly underpredicted. Jet mixing noise in cruise is much louder than predicted with relative velocity relations. Increases in the order of 20 dB are caused in cruise by stretching of the jet flow field by the flight stream. Stretching factor σ Take-off: σ ≈ 1.3 Cruise: σ ≈ 3, on future engines σ ≈ 4 AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016

AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016 Explanation of surprising properties of flight effect on jet mixing noise Jet noise much louder than originally expected from reduced relative velocity Increase of source length, coherence length and frequency range due to jet stretching Frequency not reduced in flight as to be expected from smaller relative velocities Strouhal numbers of most unstable instability waves increase with flight stream Jet noise is result of growing and decaying instability waves in jet shear layer Frequency is Doppler-shifted for observers on the ground Sources are stationary random relative to the nozzle. Moving source model of original jet noise theories incorrect. Wave model of Michalke must be used. Noise level surprisingly high in forward arc Forward arc amplification is outcome of theory for stationary sources in a flight stream AIAA/CEAS Aeroacoustics Conference, Lyon, 30 June 2016